A man walks up an escalator, taking one step per second. After taking thirty steps, he is at the top.

Next day, he goes up at two steps per second, reaching the top in 36 steps.

The third day, he has had a long afternoon and merely sits on the escalator, waiting for it to reach the top.

How long does it take him?

The first day, at one step per second, the man took thirty steps, taking 30 seconds.

The second day, at two steps per second, he took 36 steps, taking 18 seconds.

So the additional 12 seconds saved the man 6 steps, meaning the escalator traveled 6 steps in 12 seconds, or 1/2 step per second.

So when the man took 30 steps in 30 seconds, he was also carried 15 steps by the escalator, so the escalator's height is 30+15=45 steps, which is confirmed by the fact that when he took 36 steps, the escalator traveled 9 steps in the 18 seconds it took, and again 36+9=45.

At 1/2 step per second, the escalator takes 90 seconds to travel its full 45-step height, so that's how long it took the man on the third day.

Posted by Charlie on 2003-06-01 05:45:33